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  1. Jul 12, 2022
  2. Mar 03, 2022
    • Sander, Oliver's avatar
      Test (some of) the exp and log methods · c20c7471
      Sander, Oliver authored
      This triggers bugs in the Rotation and RigidBodyMotion classes.
      
      In particular, it triggers what Jonathan Youett fixed in the
      never-merged merge request
      
        !2
      
      These bugs are fixed in this commit, too:
      * The RigidBodyMotion class gets a `log` method
      * The Rotation<3>::log method now returns EmbeddedTangentVector
        instead of TangentVector.
      c20c7471
  3. May 11, 2021
    • Müller, Alexander's avatar
      changed tolerances to fix failing tests · a2647f48
      Müller, Alexander authored
      The tests failed since the construction of values of ProductManifold<> in ValueFactory uses random entries between [0.9..1.1]. These are then used for the tests and are projected onto the manifold. 
      
      To pass this tests it is needed to adjust several Taylor expansions and thresholds. For example this commit increases the threshold from `1e-4` to `1e-2` and adds more terms to the Taylor expansion. The reason for this change is explained in the following. 
      
      The problem is, even if the tolerance `1e-4` is sufficient to have a correct function value within machine precision, it is not always sufficient to get correct derivatives since here we lose orders of correctness.
      
      For  example of for sinc(x) we need to put the threshold at `1e-4` to get the correct function value if we use  `1.0-x*x/6.0` as approximation formula.
      
      If we then use this formula within automatic differentiation or finite differences, e.g. the derivative algorithms  "sees" only the following formulas of the first and second derivative:
      
      - Function value: `1.0-x*x/6.0`   This function is implemented
      - First deriv: `-x/3.0`      This sees the derivative algorithms as first derivative
      - Second: `-1.0/3.0`       This sees the derivative algorithms as second derivative
      
      Obviously, this is the case if the function value is inside the region where the Taylor expansion is used.
      
      If we use these functions to test the exactness of the derivatives we need to set the threshold to `x<1e-6` to get exact second order derivatives where the error is within machine precision. Therefore, for larger values `x>1e-6` the exact formula has to be used to get correct results. Unfortunately, in this range the exact derivative are already unstable.
      E.g. the first derivative formula behaves already strange near `x=1e-4`.
      
      Therefore,
      to get a correct derivative value we need to switch to the Taylor expansion earlier (`1e-4`) to prevent using the unstable exact formula. But in this range the Taylor expansion is unable to reproduce an approximation error within machine precision.
      
      I think the only way to fix this problem is to add more terms to the Taylor expansions. Since even if they seem to be sufficient in terms of function value, usually they are not sufficient in terms of derivatives.
      
      For `sin(x)/x` a test ist at https://godbolt.org/z/T995hGec3 and for `acos(x)^2` https://godbolt.org/z/TG9E15jjf.
      a2647f48
  4. Jan 19, 2021
  5. Nov 20, 2020
    • Sander, Oliver's avatar
      Find std math functions by ADL · 87e1da6f
      Sander, Oliver authored
      ADOL-C implements most standard math functions for its
      'adouble' type, and they are not in the namespace 'std'.
      dune-fufem contains a file adolcnamespaceinjections.hh
      which imports some of these methods into the 'std'
      namespace, but that is not the proper way to do it.
      Rather, they should be found by argument-dependent
      lookup (ADL), that is
      
        using std::sin;
        auto v = sin(x);
      87e1da6f
  6. Jan 03, 2019
  7. Feb 12, 2018
  8. Jan 15, 2018
  9. Jan 30, 2016
    • Sander, Oliver's avatar
      Implement new method distanceSquared, between a double vector and an adouble one · 6f3b9689
      Sander, Oliver authored
      This is needed for the new gradientflow application.  The standard 'distance' method
      doesn't cut it, because it is not differentiable near zero.  Therefore, even the
      differentiable expression 'distance*distance' will fail to be differentiable for
      an automatic-differentiation system.  I think in the long run we should replace
      'distance' by 'distanceSquared' everywhere it is used.
      
      Unfortunately, this patch is hacky: it only adds the method for the double/adouble
      combination.
      6f3b9689
  10. Oct 18, 2015
  11. Feb 12, 2015
  12. Sep 19, 2014
  13. Dec 13, 2013
  14. Dec 09, 2013
    • Oliver Sander's avatar
      Revert patch 9558 · 5b63350b
      Oliver Sander authored
      We normalize unit vectors again in the constructor and the assignment operator.
      This makes sure we never drift away from the unit sphere, and it also allows
      us to init unit spheres with any value in R^n and be sure we obtain a unit
      vector.  This makes the test pass again.  Leaving the projection out didn't
      really make a measurable difference anyway.
      
      [[Imported from SVN: r9574]]
      5b63350b
  15. Dec 05, 2013
    • Oliver Sander's avatar
      Do not normalize unitvectors / unit quaternions in constructors and operator= · 874cb377
      Oliver Sander authored
      This effectively means that we use another prolongation of the distance 
      function on M into the surrounding space.  Since the prolongation does not
      matter this patch should not change the algorithm behavior.  However, it
      shaves off a few norm calculations and division.  I cannot really measure
      any difference though.
      
      A possible effect of this is that while all values should remain on the
      manifold, they may start to 'drift away' due to numerical artifacts.
      So we may have to add an occasional renormalization step eventually.
      
      [[Imported from SVN: r9558]]
      874cb377
  16. Sep 03, 2013
  17. Feb 14, 2013
  18. Jan 12, 2012
  19. Nov 12, 2011
  20. Oct 25, 2011
  21. Jun 06, 2011
  22. May 23, 2011
  23. May 01, 2011
  24. Apr 25, 2011
  25. Apr 21, 2011
  26. Apr 11, 2011
  27. Apr 05, 2011
  28. Apr 03, 2011
  29. Apr 02, 2011
  30. Apr 01, 2011
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